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   "cell_type": "markdown",
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    "### Modelling primary and secondary shelf life simulatenously \n",
    "\n",
    "_this was done with 0 lit review on the subject, just out of interest_\n",
    "\n",
    "First, some simple terms: \n",
    "\n",
    " - **spoiling** is when the food product is no longer deemed consumable. \n",
    " - **primary shelf life** is the duration between a food product leaving the production facility and it spoiling on the shelf. A common censoring event for this is a consumer purchases the product (i.e., we don't observe the event of the product spoiling **on the shelf**, but rather that event is censored and we only have a lower bound on the duration).\n",
    " - **secondary shelf life** is the duration between a food product being opened by a consumer and it spoiling. For fresh produce, this could also be considered when the produce leaves the store. \n",
    "\n",
    "Below is an excellent image from \"Secondary Shelf Life: an Underestimated Issue\".\n",
    "\n",
    "![](https://i.imgur.com/klJiDHS.png)\n",
    "\n",
    "\n",
    "There are many _wrong_ ways to model primary shelf life. A first approximation to model the primary shelf life is to treat purchase events as independent censoring. This has a few important flaws:\n",
    "\n",
    " 1. discarding of information: when estimating the primary shelf life distribution, there is information included in its secondary shelf life. For an extreme example, suppose that almost every product is purchased by a consumer, and hence we see very few spoilages, and they happen very early. This makes estimating the survival curve farther out very difficult, as we have no information about lifetimes in that area. If we can observe the remaining lifetime, we can learn about the tail of the primary shelf life better.\n",
    " 2. Assumption of independence between censoring distribution and duration distribution. Consumers are more likely to purchase \"fresh-looking\" produce, and tend to purchase products with a further out expiry date compared to a near expiry date. Thus, consumer-purchase censoring events are not independent of products' current shelf life. \n",
    " \n",
    " \n",
    " Likewise, modelling the secondary shelf-life can be difficult: \n",
    " \n",
    "1. Like above, discarding of information occurs. The duration of the product in the store is highly correlated with the condition of the product, and hence is useful to untangle the secondary shelf life. Suppose that a product spoils after 7 days, but the store offers the product at a steep discount on day 6, increasing purchases. The secondary shelf life would have a dramatic drop at day 1 if we ignored primary shelf life. In fact, the primary shelf life should have this drop at day 7. \n",
    " \n",
    "Based on the above, you may think that adding duration-in-store as a covariate in a survival model would be sufficient, but the problem goes deeper: \n",
    " \n",
    "2. Frailty and immortal time bias: suppose we wish to compare the effects of a treatment/attribute on secondary shelf life for a product. Suppose that the treatment/attribute causes more \"frailty\", that is, its less stable foods spoil very quickly while in the store. Thus, upon a consumer's purchase, the only remaining products available are highly stable and will have a high secondary shelf life. Treatment does cause a higher secondary shelf life, but it's caused by a bias in the data. Controlling for the age in the store would not be adequate in this case. For example, the following conclusion is wrong due to this bias:\n",
    "\n",
    "> Ontario tomatoes have a much lower secondary shelf than California tomatoes. \n",
    "\n",
    "The problem is that the worst California tomatoes spoil during transit, and these tomatoes will never be measured for their secondary shelf life. \n",
    " \n",
    " \n",
    " \n",
    " -----\n",
    " \n",
    " Where am I going with all this? The idea is to model primary and secondary shelf life together, if the data is available. This model needs to account for \n",
    " \n",
    " 1. censoring due to administration stopping time, lack of follow up and consuming product: we can't watch a can of chickpeas exist for decades, so we must stop our study somewhere. Furthermore, if we rely on consumers to report back to us, some fraction will not and we have to consider that data censored. Finally, consumers want to eat the product, and hence we may never see the spoilage date. \n",
    " \n",
    " 2. variable purchase time: consumers can purchase a product at any time during its primary shelf life. Our model should be able to handle this. \n",
    " \n",
    " \n",
    "Let $\\tau_i$ denote the time a consumer purchases / opens food product $i$. In survival analysis, it's often useful to model the hazard instead of the survival function. With that in mind, our shelf life hazard model looks like:\n",
    "\n",
    "$$ \n",
    "h_i(t) = \\begin{cases}\n",
    "                        h_1(t)  & \\text{if $t \\le \\tau_i$} \\\\\n",
    "                        h_2(t-\\tau_i) & \\text{if $t > \\tau_i $} \\\\\n",
    "\\end{cases}                \n",
    "$$\n",
    "\n",
    "This is the most general form. If we think that the same form of degradation that occurs in the store also happens in a consumer's storage, we can model this as:\n",
    "\n",
    "$$ \n",
    "h_i(t) = \\begin{cases}\n",
    "                        h_1(t)  & \\text{if $t \\le \\tau_i$} \\\\\n",
    "                        h_1(t) + h_2(t-\\tau_i) & \\text{if $t > \\tau_i $} \\\\\n",
    "\\end{cases}                \n",
    "$$\n",
    "\n",
    "For example, this model could represent risk of spoilage caused by existing microbe growth, $h_1(t)$, and $h_2(t)$ represents additional risk caused by consumer-caused contamination. \n",
    "\n",
    "\n",
    "Estimation of these models are complicated by the censoring and the case when a purchase/opened event is not observed. Nevertheless, it can be estimated with some careful coding. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>T_obs</th>\n",
       "      <th>tau</th>\n",
       "      <th>E</th>\n",
       "      <th>obs_tau</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>13.390</td>\n",
       "      <td>1.176</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.875</td>\n",
       "      <td>0.505</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.003</td>\n",
       "      <td>14.003</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13.047</td>\n",
       "      <td>0.720</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.075</td>\n",
       "      <td>1.075</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    T_obs     tau      E  obs_tau\n",
       "0  13.390   1.176   True     True\n",
       "1   0.875   0.505  False     True\n",
       "2  13.003  14.003  False    False\n",
       "3  13.047   0.720   True     True\n",
       "4   0.075   1.075  False    False"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"shelflife.csv\")\n",
    "df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x126f68b00>"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 370,
       "width": 592
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "fig = plt.figure(figsize=(10,6))\n",
    "ax = fig.subplots()\n",
    "\n",
    "for i, row in df.loc[:25].iterrows():\n",
    "    if row['obs_tau']:\n",
    "        primary = ax.hlines(i, 0, row['tau'], color='r')\n",
    "        secondary = ax.hlines(i, row['tau'], row['T_obs'], color='r', ls=\":\")\n",
    "        purchase = ax.scatter(row['tau'], i, color=\"r\", marker=\"s\", s=12)\n",
    "    else:\n",
    "        primary = ax.hlines(i, 0, row['T_obs'], color='r')        \n",
    "    m = \"\" if not row['E'] else \"o\"\n",
    "    spoilage = ax.scatter(row['T_obs'], i, color=\"k\", marker=m, s=12)\n",
    "    \n",
    "    if i == 0:\n",
    "        primary.set_label('primary shelf life')\n",
    "        secondary.set_label('secondary shelf life')\n",
    "        purchase.set_label('opened/purchased event')\n",
    "        spoilage.set_label('spoilage event')\n",
    "\n",
    "plt.xlabel(\"time\")\n",
    "plt.xlabel(\"subject ID\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " For computational reasons, it's better to express the model as a cumulative hazard:\n",
    "\n",
    "$$\n",
    "H_i(t) = \\begin{cases}\n",
    "                        H_1(t)  & \\text{if $t \\le \\tau_i$} \\\\\n",
    "                        H_2(t-\\tau_i) & \\text{if $t > \\tau_i $} \\\\\n",
    "\\end{cases}                \n",
    "$$\n",
    "\n",
    "Let's give our model a parameteric form:\n",
    "\n",
    "$$H_1(t) = \\alpha t$$\n",
    "\n",
    "$$H_2(t) = \\left(\\frac{t}{\\lambda}\\right)^{\\rho}$$\n",
    "\n",
    "That is, our primary shelf life is modelled by a constant hazard, and the secondary shelf life is modelled by a Weibull. Below is all the code that is needed to estimate the parameters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.8866729   2.58703293  0.92460643]\n"
     ]
    }
   ],
   "source": [
    "from autograd import grad, elementwise_grad, value_and_grad\n",
    "from autograd import numpy as np\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "def H1(params, t):\n",
    "    log_alpha = params[0]\n",
    "    alpha = np.exp(log_alpha)\n",
    "    return t * alpha\n",
    "\n",
    "def H2(params, t):\n",
    "    log_lambda, log_rho = params\n",
    "    lambda_, rho = np.exp(log_lambda), np.exp(log_rho)\n",
    "    return (np.clip(t, 1e-4, np.inf) / lambda_) ** rho\n",
    "\n",
    "def cumulative_hazard(params, t, tau): \n",
    "    #return np.where(t < tau, H1(params[:1], t), H1(params[:1], tau) + H2(params[1:], t-tau))\n",
    "\n",
    "    # does the product keep degrading in the same manner when owned by the consumer?\n",
    "    # recall that hazards are additive\n",
    "    return np.where(t < tau, H1(params[:1], t), H1(params[:1], t) + H2(params[1:], t-tau))\n",
    "\n",
    "hazard = elementwise_grad(cumulative_hazard, argnum=1)\n",
    "\n",
    "def log_hazard(params, T, tau):\n",
    "    return np.log(np.clip(hazard(params, T, tau), 1e-15, np.inf))\n",
    "\n",
    "\n",
    "def survival_function(params, T, tau):\n",
    "    return np.exp(-cumulative_hazard(params, T, tau))\n",
    "\n",
    "\n",
    "def negative_log_likelihood(params, T, E, tau):\n",
    "    n = T.shape[0]\n",
    "    ll = 0\n",
    "    ll += log_hazard(params, T, tau).sum()\n",
    "    ll += -cumulative_hazard(params, T, tau).sum()\n",
    "    return -ll/n\n",
    "\n",
    "\n",
    "results = minimize(\n",
    "    value_and_grad(negative_log_likelihood), \n",
    "    x0=np.array([0.0, 0.0, 0.0]), \n",
    "    args=(df['T_obs'].values, df['E'].values.astype(bool), df['tau'].values),\n",
    "    jac=True)\n",
    "\n",
    "print(results.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12adf65f8>"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 291,
       "width": 385
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 30, 300)\n",
    "\n",
    "for t in [5.0, 10., 15.0]:\n",
    "    y = [survival_function(results.x, _, t) for _ in x]\n",
    "    plt.plot(x, y, label=r\"$\\tau=%d$\" % t)\n",
    "\n",
    "\n",
    "plt.title(\"Estimated survival function of \\nproduct to be purchased at different times\");\n",
    "plt.xlabel(\"time\")\n",
    "plt.ylabel(\"survival\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'survival')"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 277,
       "width": 385
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "time = 5.0\n",
    "x = np.linspace(0, 30, 300)\n",
    "y = [np.exp(-H1(results.x[:1], _)) for _ in x]\n",
    "plt.plot(x, y)\n",
    "plt.title(\"Estimated primary shelf life survival function\" );\n",
    "plt.xlabel(\"time\")\n",
    "plt.ylabel(\"survival\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'survival')"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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20DpJXd9jqDmeOpH5/yKmLbmrUfa1gZ9ZQywLE/FMHg6Hya1JxcZfdvctdXYZ5+4bqDnm063zUXffpMfnMDF/kuDxmCMILlIYQQXa2P9jbF/qc36PUl3/72LH2KoMF5caQ+ycWpvzeNfwrnCy+pxj8paSAWkS7n4/QeWdC4BnCFoi6ENQuWe8mV0RXXR1Y2bdgHsJTiSPEFw9ae3und19a3ffmppHdFKdpLYk9n+5qhZ3YMybsAM4d/8Zwa3V3xBcYd8IjCCoX/FFUpNtieeXzrXYjz5ZDLV1FtfV2K4muBK8lODxkB7u3tbdu4fHUq+EZdMdT1Vppie6NxyeZGatwr9jicEr7v51ijIZufv1wECCyvQvE1yJHUTQcsznZpbNToVix9NRtfy/mJPFbTe1RtvXJv7MYmpzfMYe6fiWhc1nho+VHp80vy5iZY4IH7/EzDoB382wzp8QPBqzjqChiG3dvbW7d0s4v8cuttTn/C61l0vn8ZymZECajLsvdvc73f1Igsx/D4IWMwy43syGRRpg7X2X4Bbz58BJ7j4+xTPtPTYvVmuxK8Ed07WlnEHsCnGm29cNurXt7lPc/Rp3P4DgyuX3CR7Fagc8mPB8buIV7e3quJlY2bqUS7w6nqlc7NGljFfT67Hd0tgPjjTSve/HhcNfuPtD7r4kaX5DjqU4dx9HULG6C3C4mRUR3OEBuL8B653t7n9w90PCdR8AvElwR+3PaZ4Br4/6HBO5qlH3tY6fWWU4zPTDrK7nqVQxfQF8TPB9EKsjMIrgLslagotIdfUaQYMW7QgeDYKgaeUSggrAqR6vi/0/Xu/uf0xOksP6GVvVI5aGiiVU6T6HBn8GKcSOw9J6fBc1ROycWpvz+LI6Pt4oKSgZkEh44COCE+/XBMfitxMWid9STnMLMEqxk9DkVLe+w3gPzFA+duJKt18fE3wBG3BImmXS+SQcjjCzjmmW2b+O60zL3cvd/XlqvkC3IWhmFHefTc2XyXdTFM8kVrm7i5ntlXHJGrMIKvZBTYXeTYRXGkeFo5+kWqYeJhB8psnHcOJ2dyD9F1vseJqQZv53GhTdpv4WDn9E0LRiD4K7dPX5obUZd68Kk47DCJ7xbkdw5ywbYj/c6nos5aIm29dafGax/6nepBCe70ZmKZzYlfqTwmHscZ5nPHWDABmFjwA9mmadD29eAtjy/+M+RHPFOuPnQND0crYlfhfV5ViMfS/W97s7dm5OeR4Pxb5js3Uez2tKBqTRmVlJunnhyTp2Vb1VwqyyhL870bzEnp0ckiZR+QlBhbd0YvuWcr88aLHhiXD0N1uopFsUPnMe80q4/lbUVGJOXL6E4HGAOsv0ORLUB4lJ/BzHhsOLzSzxcZfkdVt4+x4Ad59GTYsPNyW3BpJKeHUo9ozw+Wmu0p9J8NiNU7fKiJm2u5yaymyXpjkmLs+witjxNDR5RvjZXtmwCDcxluDLfUxCTP/woHWqOtnC8RBrAx82PR4aYmw4PNgSeixPxcxyvWLg2HCY1X2t52cWa4Bh9xT1ggBOZtPK/w3xb4IfkkPDumSx1sHq84hQTKzswWY2mJofmOnWmen/sYigmdMoxD6HI5JnhI/9XZDtDbr7GoK79wDXZfouShL7jqvv3YRYS0HfTVWnMKzrFGtx6NHk+VJ3SgakKdxgZo+b2ZEWNMMIgJn1MLO7COoSODXNceJBa0Sx5zJTNYcYpf8RxDsEuCv2I9aCrtMvIehYZ1mG8lPC4amWvknAywl6cRwIvGtmh8R+EIc/nAeY2YUE7ZDHr+KFFVhvCkevMbMLLWhGj/A53Keo/xf3/8zsLjPbL7bOcL07U/PjZSGbtt70B4Ir9luF+3F8UtntzOynBFd3jmRTFxL8ONkXeMnMdkso18HMTjSzfyaVuYHgkYKewAtmtmO4fCsz+wlwV7jc39x9Zt3fgrSuJTgmRgNjzaxHuN1SM7uBoH+DdBXwYsf9bWa2fyyZMLPdCVriylprL+6+CHie4Nwfu+NS30eEHjKzB8zs4MQfCeFx9iDB1dP1wFv1DjiBu79EkOwZ8JSZXRLW34ltt0t4jnmWNE3y5opG3Nf6fGbvEJyLS4CHw7tcmFlbM/sZQV2UFWRB2NjDuHD0PoLGBZYRXOSo7zo/IGg2t4SgVa1Cgru6U9IUif0/Xm1mR8TO0RY0d/wcweOtmRoKaCyxH70/MbMzwgQgdv59kcZr2egKgsq4A4E3zeyA8A4rZtbGzA41sxeTynxBcJGv1MyOoe4eIWigA+BpM/tOwnlxNMH+FhN8lyZ/B0h9eDPo7ECv3HhRt07H7kwodwc1nYA4wY+isqRpV6TY3nUJ89cQdE0+B7ggRUzXJpXtEytbi/25Ns38tOsg+AJOjH8FwQ/XWBNssU5yxqYoe0ZCufUEvSnOYfNemHcnaE0htmw5QSXTjUnb3j+pXBE1PSw7wUl5RcLfRyfM61OHz39iQrkqgmRlfcK0tcDoFOX6E9SviC1XGe7HOjbdj9NSlD2Rml6DY53mLKOmt985Kcp8PymuFdR0UOMEyVy7FOXGkaHTn3CZOeEyo1LMuyRhG9Xh+1MZjt+abv0ETaJ+k3RMxHpRXkdwFT/l58UWjuE0+3Bowvo+bsD5IPEYqw7f57VJn/MpSWVOD+eNy7Dea0n/v9OOmp55E7ebfD55oLbbrU1MW3gf0n2ufWLx1OXc0tB9zfZnFpY7iprzW+wcHusd/G/pjkNq2flUUpkfJ+1fxg7S0v1vJC1zfdI603acSFCH4suEZcup6aCyMjxe5pDiPNCQYyndcZQwv5jg8cnE83osrmUEdwzSHW8Z1x0uk3KfwnkHUPMd4gTn5KXUnN9SbfPBhOVXUvP9fWxt4iL43piTsI61ScfqV8DAFOWuJc35I2GZlMdrPr90Z0DqozadjiXeHrydoFWGZ4AZBFe7WhG0u/4IQS+AqTpl+g1wGcEVAgO2D1+RPzbk7hcSXO2dQPDjvDD8+wKCH1uVGco+QPAo0YfhctsS7NdWSct9RNDKx2XAuwQ/EDsR/ED8mOAq9/4eNBeYWK6S4Pb6eQTvXSXBF/kL4fJPUj9nAtcQtP08l6CjKgjuTvyJoKfIV5MLedDJzS7A2WHZFQTHR2UY318J3rN/pCj7b2BwuP4Z4eSicJv3AZu1fOLuzxHc4r+X4MukLcF79jbBZ3awZ24CtF7c/WaC52pfJ/isigg+p1PdPe2jWR70QbAHwf4vITiWVhJc8drdM3cmVh8vEbwf0ICKwwR3ry4N1zeL4MprIcFV2AeAXd397w1Y/2bcfa27H0XwfPuTBFes2xKck74kuHp6BvCLbG43Co20r/X6zNz9KYKk9HWCq8SFBBcHfuzuP67P/mXwBME5NaYhjwilWoeTvr4AHjz2txfwF2qar1xPkEjt7+5jsxBPnXnQSMVBBJ23zSFI5tYS/LAdSYZ+HLKw7deBHYEbCfrlqSS4izST4L08PEWxs4DfE5yrW1Hz/d0+xbKptvklMJzgd0BiX0CfESR3w9x9RqqyUncWZkkiIpIHzGwfgsRoA7CNb9pBoIiI5BndGRARyS9nhcPHlAiIiIjuDIiI5AkzO5jgcbFCYDd3Hx9xSCIiErGiqAMQEZHGZWZzCOp4xDqT+rsSARERAd0ZEBFp8cws1gLHfIJK+1e7+/rMpUREJB8oGRARERERyVOqQCwiIiIikqeUDIiIiIiI5CklAyIiIiIieUrJgIiIiIhInlIyICIiIiKSp9TPQCMxs9lAR2BOxKGIiIiISMvWByhz9x3qWlDJQOPp2KZNmy6DBw/uEnUgIiIiItJyTZ06lfXr69d9jJKBxjNn8ODBXcaPVyefIiIiItJ4Ro4cySeffDKnPmVVZ0BEREREJE8pGRARERERyVNKBkRERERE8pSSARERERGRPKVkQEREREQkTykZEBERERHJU0oGRERERETylJIBEREREZE8pWRARERERCRPKRkQEREREclTSgZERERERPKUkgERERERkTyVc8mAmR1rZn80s7fMrMzM3Mz+Uc919Taz+81sgZltNLM5ZnaHmXXOdtwiIiIiIs1NUdQB1MNVwHBgDfA1MKg+KzGzfsC7QHfgGWAasAdwPnCIme3j7suyErGIiIiISDOUc3cGgF8CA4GOwM8bsJ4/EyQC57n7ke5+ubsfCNwO7Aj8rsGRioiIiIg0YzmXDLj76+7+hbt7fdcR3hUYA8wB7k6afQ2wFjjFzNrVO9CIVFRVU1FVTXW104C3SERERETyQC4+JpQNB4TDV9y9OnGGu682s3cIkoW9gFczrcjMxqeZVa/Hlxrql49M5PnJC+PjBQYFZhQUGIVmwXiBUWBGYYFRXGi0LSmiTXEhbUsKaVMSDNuWFNGmpJD2rYro3LaELu2Kw2EJnduVsFW7VnRsU4SZRbGbIiIiIpIF+ZoM7BgOZ6SZ/wVBMjCQLSQDzU110t2Aag+nVWe6S7CxXttqU1xIz06t6dmpDduUBsOendrQd6t29OvWns7tSuq1XhERERFpGvmaDJSGw1Vp5semd9rSitx9ZKrp4R2DXeseWsNYeMW/2p3GfkpofUUVM79Zy8xv1qac37ltMf26tadvtyA52KlnR4b0LFWSICIiItJM5Gsy0GLdfVJN/uHuVFV7/O5AdeJ4tVPlTnllNevKq9hQUcW68irWlVeyvjz8u6KK1RsqWLmugmVrylmxrpzla4PhkrKNrK+oyhjLinUVfPzVCj7+asUm03t3bsPQXqUM6VXK0F6ljNiuEx1bFzfK+yEiIiIi6eVrMhC78l+aZn5s+somiKXRmBlFhY3zTL+7U7a+kgWr1rNg5XoWrNrAwpXrmbdiPbO+WcOsb9amTRa+XrGer1es5z+fLQKCeg079ezInjt0Za++XdmjTxdK2yo5EBEREWls+ZoMTA+HA9PMHxAO09UpyHtmRmnbYkrbFjN4m46bza+udhaWbWDWN2uYuWQN0xevYcqCVUxbuJryqupNl3X4bH4Zn80v429vz8YMBm3dkX0HbMWBg7ozcvvOFBfmXMNXIiIiIs1eviYDr4fDMWZWkNiikJl1APYB1gHvRxFcS1BQYPTq1IZendqw74Bu8enlldXMWLyaz+av4tP5q5g4byVTF5ZtUr/ZHaYuLGPqwjL++uYsOrYuYv8duzN6UHf2H9hNdQ5EREREsqRFJwNmVgz0AyrcfWZsurvPNLNXCFoMOgf4Y0Kx64B2wD3unrpmrNRbSVEBQ8L6AieG08o2VPDxnOW8P2s5H8xaxmcLyqhKyA7KNlTy3KQFPDdpAQUGe+zQhcOH9+K7Q7ZWYiAiIiLSAJZrHVOZ2ZHAkeHo1sDBwCzgrXDaUne/OFy2DzAb+Mrd+yStpx/wLkEvxM8AU4E9CfogmAHs7e7LGhDn+F133XXX8ePTdUMg6azZWMkHs5bx+vQlvDZ1CQtWbUi5XFGBsf/Abhw+oicH7dSDtiUtOrcVERERSWnkyJF88sknn6Rr5TKTXPz1NAI4LWla3/AF8BVw8ZZWEt4d2A34DXAI8D1gIXAncJ27r8hUXhpP+1ZFjB7cg9GDe+BHONMWrea1aUt4depiJsxbGW8ytbLaeXXaEl6dtoQ2xYUcvHMPTtpze3bv01mdoYmIiIjUQs7dGcgVujPQOJas3sALkxfyzMQFTJyXurGn/t3bc/Ke23H0Lr3VKpGIiIi0eA25M6BkoJEoGWh8Xy1by3OTFvDMxAV8sWTNZvNbFxdw2LCe/HCv7Rmx7Rb7jxMRERHJSUoGmiElA03H3ZmyoIx/fTiXZybMZ2355v0b7NGnCz/bvy8H7NidggI9QiQiIiItR77VGRDZhJkxpFcpNxw1lCu+N5hnJs7nH+/PZerCsvgyH85ZzodzljOwR3t+ul8/Dh/ek5Ii9V0gIiIi+U2/hqRFad+qiJP33J4Xz/s2T529N0fv0ouihDsBMxav4eLHJrHfTa9z75uzWFdeGWG0IiIiItFSMiAtkpmxy3adue2EEbx56QGc+e0daFdSGJ+/qGwDv3txKvvdNI6x78xmY+XmjxaJiIiItHRKBqTF69mpDVcdthPvXj6aSw7eka3a13RUtnTNRq597nMOvOUNHv1oHsTPnX8AACAASURBVJVV1RnWJCIiItKyKBmQvFHatphzDujP25cdyPVHDmHrjq3j8+avXM+lT0xmzO1v8uykBVRXq2K9iIiItHxKBiTvtC4u5JS9tmfcJaO46tDBdG1Xc6dg1tK1nPfwBI7+y7tMmKt+50RERKRlUzIgeat1cSFn7tuXNy89gIvHDKRD65rGtSbOW8lRf36XCx+dyOKyDRFGKSIiItJ4lAxI3mvXqohzDxzA25ceyM9H9aOksObf4slP5nPALeO4+/Uv2VChSsYiIiLSsigZEAmVti3mskMG8b8L9+fgnXvEp68rr+Lml6cz5vY3eX3akggjFBEREckuJQMiSbbr2pZ7TtmNf565JwN7tI9Pn7t8HWeM/YjzHp7A0jUbI4xQREREJDuUDIiksU//rXjxvH35zRE7U9qmOD792UkL+M5tb/DE+K9xV6tDIiIikruUDIhkUFRYwKnf6sPrF4/iqF16xaevXFfBRY9N4tT7P2Te8nURRigiIiJSf0oGRGqhS7sSbj9hBA/+aA96dWoTn/7WF0sZc/ubPPDObPVNICIiIjlHyYBIHew/sBuv/HI/fvztHSiwYNr6iique+5zTnvgQxatUjOkIiIikjuUDIjUUbtWRVx92E48efY+DNq6Q3z6W18s5eA73uSFyQsjjE5ERESk9pQMiNTTiG078ey53+as/fth4V2CVesrOOdfn3DhIxMp21ARbYAiIiIiW6BkQKQBSooKuPy7g/j3T/bapC7BkxPm89073uLD2csjjE5EREQkMyUDIlmwZ9+u/OeCfTk6ocWh+SvX84N73+cv42aqcrGIiIg0S0oGRLKkY+tibjthBHeftGu8X4KqaufGl6bxk4c+ZuW68ogjFBEREdmUkgGRLDt02Da8dMG+7LZ95/i0V6ct4dC73mbivJURRiYiIiKyKSUDIo1gm9I2PPzTvfjpfn3j0+avXM9x//cuD747Rz0Xi4iISLOgZECkkRQXFnDF9wbz11NG0qF1EQAVVc41z07hFw9PYF15ZcQRioiISL5TMiDSyMbsvDUv/GJfhvTqGJ/2/OSFHPd/7zF/5foIIxMREZF8p2RApAls17Utj5+1NyfvuV182pQFZRzxp7f5eI6aHxUREZFoKBkQaSKtiwv53VFD+f3RQykqCHopW7qmnB/c+z6PfjQv4uhEREQkHykZEGliP9hjO/555p50aVcCBPUILn1iMtc9N4XKquqIoxMREZF8omRAJAJ79u3KM+fsw6CtO8SnPfDOHM4Y+xFlGyoijExERETyiZIBkYhs26UtT/x8bw7euUd82ltfLOX4/3uPhatUsVhEREQan5IBkQi1a1XEX04eyXmjB8SnTVu0mqPufpdpi8oijExERETygZIBkYgVFBgXHjSQW44bHq9YvKhsA8f95T3e/XJpxNGJiIhIS6ZkQKSZOHZkbx44Y3fatwo6KFu9sZLTHviQpyfMjzgyERERaamUDIg0I/sO6MajP/sWPTq2AoKWhi54ZCJ3v/4l7h5xdCIiItLSKBkQaWZ26tmRp87eh4E92sen3fzydH77wlQlBCIiIpJVSgZEmqGendrw2Fl7s1ffLvFpf3t7Npc/8SlV1UoIREREJDuUDIg0U6VtinnwR3vw3SFbx6c98vE8znt4AuWV6pxMREREGk7JgEgz1qqokD/+YBeOHdk7Pu2FTxfyk4c+Zn15VYSRiYiISEugZECkmSsqLOCmY4Zx+t594tPemPENp97/gXorFhERkQZRMiCSAwoKjGu+vxPnJ3RO9tGcFfzgr++zfG15hJGJiIhILlMyIJIjzIxfHjSQqw4dHJ82ZUEZJ92rhEBERETqR8mASI45c9++3HjMUCzorJhpi1Zz0r3vs2zNxmgDExERkZyjZEAkB52w+3bcetzwTRKCk+/7QAmBiIiI1ImSAZEcdfSuvbnt+OEUbHKH4AOWKiEQERGRWlIyIJLDjtqlN7cdPyKeEExfHDwypIRAREREakPJgEiOO3KXXtx+Qk1CMGPxGiUEIiIiUitKBkRagCNGbJ4QnPK3D1m1Tv0QiIiISHpKBkRaiOSEYOrCMk574EPWbKyMNjARERFptpQMiLQgR4zoxU3HDo+PT5y3kjMf/IgNFVURRiUiIiLNlZIBkRbm2JG9uf6InePj789azln/GE95ZXWEUYmIiEhzpGRApAU65Vt9uPy7g+Lj46Z/w/n/nkBllRICERERqaFkQKSFOmv/fpx3YP/4+H8+W8SlT0ymutojjEpERESaEyUDIi3YLw8ayI/22SE+/uQn87nuuSm4KyEQERERJQMiLZqZcfVhgzlx923j0x587yv+PG5mhFGJiIhIc6FkQKSFMzN+d9RQDh22TXzazS9P55GP5kYYlYiIiDQHSgZE8kBhgXHb8cPZu1/X+LRfPfkp//18cYRRiYiISNSUDIjkiVZFhdxzykh27tkRgGqHc//1CR/PWR5xZCIiIhIVJQMieaRD62LGnrEH23VpC8DGymp+NPYjZixeHXFkIiIiEgUlAyJ5pluHVjz0oz3Yqn0JAGUbKjn1bx8yf+X6iCMTERGRpqZkQCQP9dmqHWPP2IN2JYUALCrbwBkPfEjZhoqIIxMREZGmpGRAJE8N6VXKX0/djeJCA2DG4jX8/B/jKa9UL8UiIiL5QsmASB7bp/9W3Hzs8Pj4O18u48qnPlWnZCIiInlCyYBInjtyl15cdNDA+Phj47/mT699GWFEIiIi0lSUDIgI5x7Yn2NH9o6P3/rfGTw9YX6EEYmIiEhTyMlkwMx6m9n9ZrbAzDaa2Rwzu8PMOtdxPd82s2fC8hvMbK6ZvWhmhzRW7CLNkZlxw1FD2ad/Tadklz4+mfdnLYswKhEREWlsOZcMmFk/YDxwBvAhcDswCzgfeM/MumYonrienwNvAaPD4e3AG8D+wH/M7MrsRy/SfJUUFfDnk0cysEd7AMqrqvnZ38cz85s1EUcmIiIijSXnkgHgz0B34Dx3P9LdL3f3Awl+zO8I/G5LKzCzYuD3wAZgpLuf4u6/cvdTgN2AjcCVZtaq0fZCpBkqbVPM/afvTrcOwaG/an0FPxr7ESvWlkccmYiIiDSGnEoGwrsCY4A5wN1Js68B1gKnmFm7LayqC1AKzHD36Ykz3H0qMANoA7TPQtgiOaV357bcf9rutCkO+iD4atk6fv7P8VRUqclRERGRliankgHggHD4irtv8svE3VcD7wBtgb22sJ4lwDfAQDMbkDjDzAYCA4CJ7q4HpiUvDe1dyu0njIiPvz9rOdc8O0VNjoqIiLQwuZYM7BgOZ6SZ/0U4HJhmPgAe/KI5h2D/x5vZg2b2ezN7iKA+whTguNoEZGbjU72AQbUpL9JcHTJkay45eMf4+L8+mMtD730VYUQiIiKSbUVRB1BHpeFwVZr5semdtrQid3/MzBYADwOnJsxaDDxAUClZJK+dPaofMxav5pmJCwD4zfOf07dbO/Yd0C3iyERERCQbcu3OQNaY2Q+B/xG0JDSY4PGiwcCrwJ+Af9dmPe4+MtULmNZIoYs0GTPjxmOGMXzbIL+uqnbO/ucnamFIRESkhci1ZCB25b80zfzY9JWZVhLWC7if4HGgU9x9mruvd/dpwCkEjwodZ2ajGh6ySG5rXVzIvaeMZOuOrQFYvaGSMx/8mFXrKiKOTERERBoq15KBWMs/6eoExCoDp6tTEDMGKAbeSFERuRp4MxwdWZ8gRVqa7h1bc99pu9G6ODhlzF66lnP+9QmVamFIREQkp+VaMvB6OBxjZpvEbmYdgH2AdcD7W1hPrP+AdA8+x6arcXWR0JBepdx2fE0LQ29/uZSbXp6eoYSIiIg0dzmVDLj7TOAVoA9Ba0CJrgPaAX9397WxiWY2yMySW/Z5Kxwea2bDEmeY2QjgWMCB17IXvUju+97QbTh/dE1rvH99cxbPTJwfYUQiIiLSELnWmhDA2cC7wF1mNhqYCuxJ0AfBDODKpOWnhkOLTXD3D83sAeAM4CMzewr4iiDJOBIoAe5w9ymNuB8iOen80QOYsqCM/01dDMBlT0ymf/f27NwzXVUeERERaa5y6s4AxO8O7AaMJUgCLgL6AXcCe9Who7AfEyQD7wEHh+s5CHgb+IG7/zK7kYu0DAUFxu0nDKdvt6Cj7w0V1fz0ofEsX6un6kRERHJNziUDAO4+z93PcPdt3L3E3bd39wvcfUWKZc3dLcV0d/ex7j7K3Tu7e5G7d3H30e5eq2ZFRfJVh9bF/PWU3WjfKri5OH/les5VhWIREZGck5PJgIhEr3/39txxQk2F4ndnLuMP/1H3GiIiIrlEyYCI1Nt3durBL79T09LvfW/PVoViERGRHKJkQEQa5BcH9mfMTj3i45c+PpmpC8sijEhERERqS8mAiDRIQYFx6/HD6d+9PQAbK6v5+T/GU7ZBPRSLiIg0d0oGRKTBOrQu5v9+OJJ2JYUAzFm2josfnYS7RxyZiIiIZKJkQESyon/39tx4bE0ffq98vph735oVYUQiIiKyJUoGRCRrDhvWk9P37hMfv/Gl6Xwwq7Zdf4iIiEhTUzIgIll1xfcGs+t2nQCoqnbOfXgCS8o2RByViIiIpKJkQESyqqSogLtP3pUu7UoA+Gb1Rs59eII6JBMREWmGlAyISNZtU9qGP/5gFwrCvr8/nL2cm1+eHm1QIiIishklAyLSKPbpvxUXHlTTIdk9b87ipc8WRRiRiIiIJFMyICKN5uxR/TlwUPf4+CWPTWL20rURRiQiIiKJlAyISKMpKDBuO344vTu3AWD1xkp+/o/xbKioijgyERERASUDItLIOrUt4S8nj6SkMDjdTFu0muue+zziqERERASUDIhIExjau5RrD985Pv7wh3N5dtKCCCMSERERUDIgIk3kB3tsy/eH94yPX/Hkp8xR/QEREZFIKRkQkSZhZtxw1BC279oWgDUbKzn34U/YWKn6AyIiIlFRMiAiTaZD62LuPmnXeP2Bz+aX8fsXp0UclYiISP5SMiAiTWpIr1Ku+N6g+PjYd+eo/wEREZGIKBkQkSZ32t59GLNTj/j4pY9PYt7ydRFGJCIikp+UDIhIkzMzbj52OL06Bf0PlG2o5BcPT6CiqjriyERERPKLkgERiURp22L+eNIuFBUYABPnreSWl6dHHJWIiEh+UTIgIpHZdbvOXHLwjvHxe96cxWvTFkcYkYiISH5RMiAikfrJvn05YMdu8fGLHp3EwlXrI4xIREQkfygZEJFIFRQYtx4/gh4dWwGwYl0FFz4yiapqjzgyERGRlk/JgIhErku7Eu46cRfC6gO8N2sZ97w5M9qgRERE8oCSARFpFvbs25VzD+gfH7/tlRlMnLcywohERERaPiUDItJsnDd6ALtu1wmAymrn/H9PYM3GyoijEhERabmUDIhIs1FUWMCdJ+5Ch1ZFAHy1bB2/fuaziKMSERFpuZQMiEizsm2Xtvz2qCHx8Sc/mc8zE+dHGJGIiEjLpWRARJqdI0b04uhde8XHr3rqM+YtXxdhRCIiIi2TkgERaZZ+c8QQtu/aFoDVGys5798TqKyqjjgqERGRlkXJgIg0S+1bFXHnibtQFLY3OmHuSu569YuIoxIREWlZlAyISLM1YttOXDhmYHz8T69/yQezlkUYkYiISMuiZEBEmrWf7dePb/XtCkC1wy8fmciqdRURRyUiItIyKBkQkWatsMC4/YQRdGpbDMCCVRu44ulPcfeIIxMREcl9SgZEpNnburQ1Nx4zLD7+wuSFPK3mRkVERBpMyYCI5ISDd96aE3ffNj7+66en8PUKNTcqIiLSEEoGRCRnXH3YTps0N3rRo5OoqtbjQiIiIvWlZEBEcka7VkXcfsIICsPmRj+YvZz73poVcVQiIiK5S8mAiOSUXbfrzDkH9I+P3/LKdD5fUBZhRCIiIrlLyYCI5JxfHNif4b1LAaioci54ZAIbKqoijkpERCT3KBkQkZxTXFjA7SeMoE1xIQAzFq/hppemRxyViIhI7lEyICI5qW+39lx56OD4+P3vzObtL5ZGGJGIiEjuUTIgIjnr5D2348BB3ePjFz82iZXryiOMSEREJLcoGRCRnGVm3HjMMLq2KwFgUdkGrnr6M/VOLCIiUktKBkQkp3Xr0Io/JPRO/PzkhTwzcUGEEYmIiOQOJQMikvMO2qnHJr0TX/30Z+qdWEREpBaUDIhIi6DeiUVEROpOyYCItAjtWhVx2/EjCDsnVu/EIiIitaBkQERajJHbd+bcAwfEx299ZQbTF62OMCIREZHmTcmAiLQovziwP8PC3onLq6q58NGJlFdWRxyViIhI86RkQERalOLCAm49bjglRcHpbcqCMv702hcRRyUiItI8KRkQkRZnQI8OXHrwjvHxu8fNZNK8lRFGJCIi0jwpGRCRFulH++zAHjt0AaCq2rnw0YlsqKiKOCoREZHmRcmAiLRIBQXGrccNp11JIQAzv1nLTS9NjzgqERGR5kXJgIi0WNt2actVh+0UH7//ndm8N3NZhBGJiIg0L0oGRKRFO3H3bRm1Y7f4+MWPTWL1hooIIxIREWk+lAyISItmZtx4zDBK2xQDMH/len77/NSIoxIREWkelAyISIvXo2Nrrj9ySHz8kY/n8dq0xRFGJCIi0jwoGRCRvHD48J4cOmyb+PhlT3zKirXlEUYkIiISPSUDIpI3fnvEELZq3wqAb1Zv5KpnPos4IhERkWgpGRCRvNG5XQk3HjM0Pv7C5IU8O2lBhBGJiIhES8mAiOSV0YN7cPxuvePjVz/9GYvLNkQYkYiISHRyMhkws95mdr+ZLTCzjWY2x8zuMLPO9VjXrmb2LzP7OlzXYjN7w8xObYzYRSR6Vx+2E706tQFg1foKLn9iMu4ecVQiIiJNL+eSATPrB4wHzgA+BG4HZgHnA++ZWdc6rOtc4CNgDPAqcCvwFFAIfC+7kYtIc9GhdTE3HzcsPv769G945KN5EUYkIiISjaKoA6iHPwPdgfPc/Y+xiWZ2G/BL4HfAWVtaiZmNAe4C/gsc6+6rk+YXZzNoEWle9u63FWfs04cH3pkDwPXPf84+/bdi2y5tow1MRESkCeXUnYHwrsAYYA5wd9Lsa4C1wClm1q4Wq7sZWA+clJwIALi7uigVaeEuO2QQfbsFp4u15VVc/Ngkqqv1uJCIiOSPnEoGgAPC4SvuXp04I/xB/w7QFtgr00rMbAgwDHgFWG5mB5jZxWZ2kZmNNrNce19EpB5aFxdy2/EjKCwwAD6YvZwH35sTaUwiIiJNKdceE9oxHM5IM/8LgjsHAwnqAKSzezhcAowD9kua/6mZHe3uX24pIDMbn2bWoC2VFZHojdi2Ez/fvx9/ej34d7/xpWmM2rE7O2xVmxuMIiIiuS3XroCXhsNVaebHpnfawnq6h8MfA32AQ8N1DwT+AQwFXjCzknpHKiI54xej+zNo6w4AbKio5pLHJlGlx4VERCQP5FoykC2x/S4ETnT3F929zN2/AE4FPiZIDI7Z0orcfWSqFzCt0aIXkaxqVVTILccNpyh8XOjjr1bwwDuzI45KRESk8eVaMhC78l+aZn5s+sotrCc2f5G7v5c4w4PGxp8JR/eoc4QikpOG9CrlnAP6x8dvfnk6Xy5ZE2FEIiIijS/XkoHp4XBgmvkDwmG6OgXJ60mXNKwIh21qGZeItADnHNCfnbbpCMDGymou1uNCIiLSwuVaMvB6OByT3OKPmXUA9gHWAe9vYT3vEzRD2idNM6RDwqGeExDJIyVFBdxy3HCKC4PHhSbOW8m9b82KOCoREZHGU+/WhMzstXoWdXcfXc+CM83sFYIWg84B/pgw+zqgHXCPu69NiHNQWHZawnrWmdnfgPOA35rZheHjQZjZUOB0oBJ4vD5xikju2qlnR847cAC3/je4wXjbKzMYPag7A3p0iDgyERGR7GtI06Kj6lmuoffczwbeBe4ys9HAVGBPgj4IZgBXJi0/NRxa0vSrCZoUvQD4lpm9A/QAjgZaAxe4+8wGxioiOeisUf145fPFfDp/FeVV1Vz02CSe/PneFBXm2s1UERGRzOr9zebuBfV8FTYk4PAH+m7AWIIk4CKgH3AnsJe7L6vlesqAfYEbgC7AucBhwNvAwe5+Z0PiFJHcVVxYwK3HD6ck/PE/+etV3POmHhcSEZGWJycvc7n7PHc/w923cfcSd9/e3S9w9xUpljV3T74rEJu3xt2vdPeB7t7K3Tu5+xh3f6Xx90JEmrOBPTrwy4Nq2iq4438zmLqwLMKIREREsi8nkwERkabwk313YMS2QR+GFVXORY9OoqKqOuKoREREsqdRkgEz621me5rZfqlejbFNEZFsKyoMWhcqKQpOlZ8vLOPu17+MOCoREZHsyWoyYGZjzGwK8BVBJd/X07xERHJC/+7tuWTMjvHxP732JZ/NX5WhhIiISO7IWjJgZnsBzwOdgD8RtN7zJnAvMC0cfw74Tba2KSLSFH707R0YuX1nACqrnYsfm0R5pR4XEhGR3JfNOwO/AjYAu7v7+eG01939LIJOvH4LfAe13S8iOaawwLj52GG0Lg5OmdMWreaPr30RcVQiIiINl81k4FvAs+6+IHn9Hvg1QZv/12VxmyIiTaJvt/ZcevCg+Pifx81k8tcrI4xIRESk4bKZDJQCcxPGywl6BE70DkFHXyIiOef0vfuwR58uAFRVB60LbaysijgqERGR+stmMrAE6Jw03i9pmWKgTRa3KSLSZAoKjJuPG0ab4qDvxC+WrOGO/+lxIRERyV3ZTAZmsOmP//eBg8xsIICZbQ0cA+ibU0Ry1vZd2/Gr79U8LnTPGzOZMHez/g5FRERyQjaTgZeA/c2sSzh+J8FdgAlm9hFBi0LdgDuyuE0RkSb3wz2351t9uwJQ7XDxY5PYUKHHhUREJPdkMxm4h6A+QAWAu78DHAfMJmhNaCHwc3d/KIvbFBFpcgUFxk3HDqNdSfC40Mxv1nLbf2dEHJWIiEjdZS0ZcPcyd//A3VcnTHvK3Ye4ext3H+zuf83W9kREorRtl7Zccejg+Pi9b81i/FfLI4xIRESk7rLZ6VhWezMWEWnuTtpjO/YdsBUA7nDxY5NZX67HhUREJHdk8wf8PDO70cx2zuI6RUSaLTPjxmOG0aFVEQCzl67lppenRRyViIhI7WUzGWgLXAJMNrOPzOychMrEIiItUs9Obbj6sJ3i4w+8M4f3Zy2LMCIREZHay2Yy0AM4kaBVoRHAXcACM3vCzA43s8IsbktEpNk4brfejNqxW3z80scns3ZjZYQRiYiI1E42KxCXu/uj7n4o0Bu4lKDvgaOApwgSg9vNbJdsbVNEpDkwM/5w9DA6tA4eF5q7fB03vqTHhUREpPlrlEq/7r7Y3W9192HASOCPgAPnAx81xjZFRKK0dWlrrv1+TZWph977ine/XBphRCIiIlvW6C0AufsE4G7gQYI+CKyxtykiEoWjd+3FdwZ3j49f8vhk1uhxIRERacYaLRkws1Iz+5mZvUvQ+/DFwHrg/sbapohIlMyMG44aSmmbYgDmr1zPDS9OjTgqERGR9LKaDJhZgZl9z8weIehx+M/AHsCrwCnANu7+k2xuU0SkOenesTW/OaLmcaF/fTCXN2d8E2FEIiIi6WWz07FbgfnAc8BxwFzgKqCPu49x93+5+/psbU9EpLk6fHhPDt65R3z8sicmU7ahIsKIREREUsvmnYFfAq2Be4F93H2Qu//e3b/O4jZERJo9M+O3Rw6lc9vgcaGFqzZw/XOfRxyViIjI5rKZDPwA2Nrdz3L397K4XhGRnNOtQyuuP3JIfPyx8V/z6tTFEUYkIiKyuWz2M/CIu2/M1vpERHLdYcN6ctiwbeLjlz/5KSvWlkcYkYiIyKYavWlREZF8dv0RQ9iqfSsAvlm9kWuenRJxRCIiIjXqnQyYWbWZVZrZwITxqlq81Oi2iOSNzu1K+P3RQ+Pjz05awIufLowwIhERkRpFDSj7JkGvwuuSxkVEJMFBO/XgmF1788QnQXsKVz39GXvs0CV+x0BERCQq9U4G3H1UpnEREanx6+/vxLszl7Jw1QaWry3niic/5Z5TRmKmTtlFRCQ6qjMgItIEStsUc+Mxw+Ljr3y+mKcnzo8wIhERkex2OnaTmQ3O1vpERFqa/QZ24+Q9t4uPX/PMFBat2hBhRCIiku+yeWfgYuAzM/vQzM4xsy5ZXLeISItwxfcGs22XNgCUbajksicm467qViIiEo1sdzr2MrALcBewwMweN7Pvm1lhFrcjIpKz2rUq4uZjhxOrKvDGjG945KN50QYlIiJ5K9udjn0P6A1cBnwBHA08TZAY3GZmI7K1PRGRXLVX366csfcO8fHrn/+cecvXZSghIiLSOLJegdjdF7v7Le4+FBgJ/Akw4AJgvJlNzPY2RURyzaWH7Ejfbu0AWFtexaWPT6a6Wo8LiYhI02rU1oTcfYK7nw/0BC4BKoGhmUuJiLR8rYsLufW44RSEjwu9N2sZf3//q2iDEhGRvNOoyYCZlZrZT4E3gJuAYqCsMbcpIpIrdtmuM2ft3y8+/vv/TGX20rURRiQiIvkm68mAmRWY2XfN7N/AQuAvwJ7Aq8ApBHcJREQEOP87Axi0dQcANlRUc/Fjk6jS40IiItJEstnPwFAzuxn4GngeOB6YC1wN9HH3Me7+T3dfn61tiojkulZFhdxy3HCKwueFxn+1gvvemhVxVCIiki+yeWdgEnAR0Aa4D9jH3Qe5+w3u/nUWtyMi0qIM6VXKLw4cEB+/9ZUZzFi8OsKIREQkX2QzGXgZOAnY2t1/5u7vZXHdIiIt2tkH9GNor1IAyququejRSVRUVUcclYiItHTZTAYeBla4+8YsrlNEJC8UFxZw6/HDKSkMTsufzl/FX8bNjDgqERFp6bKZDNwPHJLF9YmI5JWBPTpw0ZiB8fG7Xv2CKQtWyIKWJgAAIABJREFURRiRiIi0dNlMBhZleX0iInnnzH37MnL7zgBUVjsXPTqJjZVVEUclIiItVTZ/vL8EHGBmSghEROqpsMC45bjhtC4OTqXTFq3mrle/iDgqERFpqbL5w/1KoAPwNzPbKovrFRHJKzts1Y7LDxkUH//LuJlMmLsiwohERKSlynYF4lXAqcA8M5tqZq+b2WtJr1ezuE0RkRbp1G/14Vt9uwJQ7XDho5NYV14ZcVQiItLSZDMZGAUMAwxoBewI7B9OT36JiEgGBQXGTccOo32rIgBmL13L71+cFnFUIiLS0mQtGXD3glq+CrO1TRGRlmzbLm255vs7xcf//v5XjJu+JMKIRESkpVFlXxGRZuzYkb05eOce8fFLH5/MirXlEUYkIiItiZIBEZFmzMy44aihbNW+FQBLVm/kyqc/xd0jjkxERFqComytyMz2q+2y7v5mtrYrItLSdW3fihuPGcqPH/wYgBc/XcTTE+dz1C69I45MRERyXdaSAWAcUNtLVao3ICJSB6MH9+AHe2zHwx/OBeDXT09hjx260qtTm4gjExGRXJbNZOA3pE4GOgG7A3sDzwGfZHGbIiJ546pDB/PuzKV8tWwdqzdWcvGjk/jnmXtSUGBRhyYiIjkqa8mAu1+bab6ZnQ78kaBzMhERqaN2rYq47fjhHPd/71Ht8N6sZdz/zmzO3Ldv1KGJiEiOarIKxO4+FngfuKGptiki0tKM3L4LZ4/qHx+/6eXpTF+0OsKIREQklzV1a0ITgVpXNBYRkc2dN3oAO/fsCEB5ZTUXPDKRjZVVEUclIiK5qKmTgW3Jbj0FEZG8U1JUwB0njKCkKDiFT11Yxh3/+yLiqEREJBc1STJgZoVmdiZwLPBxU2xTRKQlG9CjA5cfMig+fs8bM/lozvIIIxIRkVyUtWTAzGalec0F1gH3ABXAFdnapohIPjt97z7s078rANUOFz46kTUbKyOOSkREckk27wwUAJbiVQF8SpAM7Oru72ZxmyIieaugwLj52OF0aB08fTlv+Xquf+7ziKMSEZFcks2mRftka10iIlI7PTu14bdHDuH8f08E4JGP5zF6cHfG7Pz/7d13nFx1vf/x12drks2SXgglIZBGlQRIkBKKIhaUJldEpBfxiiLo1WtDr/4s16siiqhXLkIQFVRERUApgnQSCBBTaGmE9EL6Zne/vz9mdrKEbOrunp2d1/PxmMeZ8z1nznx2T0523nPO+X4HZlyZJKkYtPk9AxHRJyJOiYh3RYQjD0tSK3v/QYN434G7FuY///vnWbxqfYYVSZKKRWveM/CxiHgiIno3axsDTANuB+4CHo2ImtZ6T0kSRARfP3l/BuxSDcCS1XV87nfPkdLmBoWXJGmj1jwz8G9ASik1787iv4FewP+RCwOHApfu7BtFxO4RcUNEzIuI9RExMyJ+EBG9dmKbR0dEQ0SkiPj6ztYoSe2pZ7cqvnP6QYX5v09dyIQnZmdYkSSpGLRmGBgGPNc0ExF9gfHAL1JKF6aUTgKeAj68M28SEXsDE4HzgCeB7wOvAJ8EHouIPjuwzVrgl+R6PZKkojR+eD/OffuQwvzX//wvZixwdGJJUstaMwz0ARY2mz8iP/1Ds7aHgcE7+T7XAf2By1NKJ6eUPpdSOo5cKBgBfGMHtnkN0AP45k7WJkmZ+ty7RzJyYC0A6+sbufzWZ1i3wdGJJUmb15phYCnQt9n8eKARaN6VaAK67Ogb5M8KnADMBH68yeKvAKuBs7fnvoSI+AC5swyXA/N2tDZJ6gi6VJZzzYcOLoxOPG3+Sr5z9/SMq5IkdVStGQamAiflew/qCXwIeCql9EazdYYA83fiPY7NT+9NKTU2X5BSWgk8AnQDxm3LxiKiP/Bz4I6U0oSdqEuSOowRA2v5wntGFeZveORVHpy+cAuvkCSVqtYMA9cAuwJzgTnAAHKX9DQ3Dpi8E+8xIj+d0cLyF/PT4du4vZ+T+x3s8E3NETFxcw9g5I5uU5J21kcPH8xxI/sX5q+67Tm7G5UkvUWrhYGU0p3kPlRPAaYDVzX/tj0ijgG6A/fsxNv0yE9XtLC8qb3n1jYUEecD7wcuSykt2ImaJKnDiQi+c/qB9O2e62508ar1fPZ2uxuVJL1Zq41ADJBS+hnwsxaWPUium9HMRcQQ4AfAbSml3+7MtlJKY1p4j4nA6J3ZtiTtjL7dq/mfMw7inBueBOD+aQu56bFZnNOsxyFJUmlr8xGIW1nTN/89Wlje1L58K9u5AVgLXNYaRUlSRzV+eD/OP2Kvwvw37prK9Pl2NypJyim2MNDUJUZL9wQMy09buqegyWhy3ZMuyg8yliIikRscDeAL+bY7dq5cScreZ08cUehutM7uRiVJzbTqZULt4IH89ISIKGveo1B+4LAjyA0c9vhWtnMTuV6HNjUMOBp4ltzAZs/sdMWSlLEuleVce+bBvO/af7K+vpHpC1byrb9O4+r375d1aZKkjBVVGEgpvRwR95Iba+DjwLXNFn8VqAF+mlJa3dQYESPzr53WbDuXb277EXEuuTDwl5TSF1v9B5CkjAwbUMsX37cvX7rjBQBufHQm40f049gR/bfySklSZ1ZslwlB7jr/hcAPI+KOiPhmRNwPXEHu8qAvbLL+1PxDkkraR8buyTtGDSjMf+a2ySxaaXejklTKii4MpJReBg4BbgTGAlcCe5Mb52BcSmlJdtVJUscVEXz7tAPoV9vU3WgdV902mcZGuxuVpFJVdGEAIKU0J6V0Xkpp15RSVUppcErpUymlZZtZN1JKsY3bvTG/vpcISeqU+nSv5ntnHFSY/8eMRfzin69mWJEkKUtFGQYkSTvuqGH9uPjooYX5b989jWfnbK1HZklSZ2QYkKQSdNUJIzhoj9xg7fWNiU/cOok31m3IuCpJUnszDEhSCaqqKONHZx5MbZdcp3Jzlq7l8797npS8f0CSSolhQJJK1B69u/Ht0w4szP/l+df51ZOzM6xIktTeDAOSVMLec8CunDV2z8L81/70L6bNfyPDiiRJ7ckwIEkl7kvv25eRA2sBWF/fyMdvmcSauvqMq5IktQfDgCSVuC6V5fzow6PpWlkOwMuLVvOVP07JuCpJUnswDEiS2Kd/d772gf0K87dNnMsdz7yWYUWSpPZgGJAkAXD6mN055eDdCvNf+MPzvLp4dYYVSZLammFAkgRARPBfJ+/PXn1rAFhd18DHb5nEug0NGVcmSWorhgFJUkH36gp+9OGDqSrP/Xn41+tv8LU//yvjqiRJbcUwIEl6k/0G9eCL7xtVmP/VE7P5wzNzM6xIktRWDAOSpLc4e9xgTjpoUGH+P3//AjMWrMywIklSWzAMSJLeIiL45qkHMLRf7v6BtRsa+NiEiaxe7/gDktSZGAYkSZvVvbqCn5w1hi6VuT8VLy9azed+/zwppYwrkyS1FsOAJKlFIwbW8v9OOaAw/6fJ85jw+KwMK5IktSbDgCRpi04dvTtnHrZHYf6//jyVyXOWZ1iRJKm1GAYkSVv1lZP2Y79BuwBQ19DIZbdMYvmauoyrkiTtLMOAJGmrulSWc91Zo6ntUgHAa8vXcuVvJ9PY6P0DklTMDAOSpG0yuE8N3/3gQYX5+6Yt5PqHXs6wIknSzjIMSJK22bv2G8hFR+1VmP/uPdN59KXFGVYkSdoZhgFJ0nb57IkjOWRwLwAaE/z7rc/w2vK1GVclSdoRhgFJ0napLC/jx2eNpm/3agCWrq7jYxMmsm5DQ8aVSZK2l2FAkrTdBuzShZ98ZDQVZQHAc3NX8KU7XnBAMkkqMoYBSdIOOXRIb770vn0L87dNnMuEJ2ZnWJEkaXsZBiRJO+yjhw/m1NG7Fea/9qcpTJy1NMOKJEnbwzAgSdphEcH/O+UA9t8tNyDZhobEpRMmseCNdRlXJknaFoYBSdJO6VJZzvUfGUOvbpUALFq5nstumURdfWPGlUmStsYwIEnaabv36sa1Z44mfz8xE2ct42t/npJtUZKkrTIMSJJaxZHD+vIfJ44szE94fDa/fXpOhhVJkrbGMCBJajUXHz2U9x64a2H+i3e8wOQ5yzOsSJK0JYYBSVKriQi+c9qBjBhQC0BdfSMX3fQ081d4Q7EkdUSGAUlSq6qpruCnZ4+hR9fcDcULV67n4pufdoRiSeqADAOSpFY3pG8N1501mvJmIxR/5vbnHKFYkjoYw4AkqU0csU9frj5p4wjFf5o8jx8/8FKGFUmSNmUYkCS1mbMPH8JHxu1ZmP/uvTO4+4X5GVYkSWrOMCBJalNfOWk/Dh/apzB/xW+eZcq8FRlWJElqYhiQJLWpyvIyrjtrNIP7dANg7YYGLvrl0yxauT7jyiRJhgFJUpvrVVPF/370ELpXVwAwb8U6Lp0wkfX19jAkSVkyDEiS2sWwAbVce+bBRK6DISbOWsYX/vCCPQxJUoYMA5KkdnPsyP7857tHFeZvnziXnz70SoYVSVJpMwxIktrVhUftxeljdi/Mf+uv0/jLc69nWJEklS7DgCSpXUUE3zhlfw4b0rvQdsVvn2XirGUZViVJpckwIElqd9UV5fz07DHs1bcGgLr6Ri6+6WlmL1mTcWWSVFoMA5KkTPSqqeL/zj2U3jVVACxZXce5Nz7J8jV1GVcmSaXDMCBJysyQvjX8/KNjqKrI/Tl6ZdFqLrnZLkclqb0YBiRJmRozuDffO+OgwvwTry7l87973i5HJakdGAYkSZl734GD+OyJIwrzv3/mNb7/txkZViRJpcEwIEnqED42fm/+7ZA9CvM/vP8lbnliVoYVSVLnZxiQJHUIEcHXT9mfo4f3K7R96Y4XuGfK/AyrkqTOzTAgSeowKsvL+MlZozlw9x4ANCa4/NZneHrm0owrk6TOyTAgSepQaqoruOHcQxncpxsA6+sbueCXT/PigpUZVyZJnY9hQJLU4fTtXs1N5x9G3+65MQhWrN3AOTc8yesr1mZcmSR1LoYBSVKHNLhPDf937mF0qyoHYN6KdZx7w1OsWLsh48okqfMwDEiSOqwDdu/B9R8ZQ0VZADB9wUou/OVTrK1zUDJJag2GAUlSh3b08H585/QDC/NPzVzGpRMmUlffmGFVktQ5GAYkSR3eqaN354vvHVWY/8eMRVzx22dpaHSUYknaGYYBSVJRuPCooXziuH0K83957nW+eMfzpGQgkKQdZRiQJBWNT79zOOccPrgwf+uTc/jWX6cZCCRpBxkGJElFIyL4ykn7ccrBuxXafvrQK1z34MsZViVJxcswIEkqKmVlwXdOP5B3jBpQaPvve6Zz82MzM6tJkoqVYUCSVHQqy8v40YcP5vChfQptX/rjFH771JwMq5Kk4mMYkCQVpS6V5fz8nEM4aI+ehbb/+P1z/H7S3AyrkqTiYhiQJBWt7tUV3HTeYew3aBcAUoKrbpvMnZPnZVyZJBWHogwDEbF7RNwQEfMiYn1EzIyIH0REr218fU1EnBURv4qIaRGxOiJWRsTTEXFlRFS19c8gSWodPbpVMuGCsYwcWAtAY4IrfvMsf33+9Ywrk6SOr+jCQETsDUwEzgOeBL4PvAJ8EngsIvps4eVNjgImAO8CXgCuBX4F7AZ8F3ggIrq0fvWSpLbQq6aKCReOZVj/7gA0NCY+cesz/O1fCzKuTJI6tqILA8B1QH/g8pTSySmlz6WUjiMXCkYA39iGbcwHPgLsmlI6Pb+NS4DhwCTg7cDH26Z8SVJb6Nu9mlsuGsvQvjUA1DcmLrtlIg9MW5hxZZLUcRVVGMifFTgBmAn8eJPFXwFWA2dHRM2WtpNSejaldEtKqW6T9pXA/+Rnj2mNmiVJ7ad/bRd+ddE4BvfpBsCGhsQlN0/kvqmeIZCkzSmqMAAcm5/em1JqbL4g/0H+EaAbMG4n3mNDflq/E9uQJGVkYI9cINi9V1cA6hoauXTCRO5+YX7GlUlSx1NsYWBEfjqjheUv5qfDd+I9zs9P796WlSNi4uYewMidqEGStBN269mVX188jj17bzxD8PFfTeLPz9nLkCQ1V2xhoEd+uqKF5U3tPVtYvkUR8e/AicCzwA07sg1JUsewe69u/OaSceyVv4egoTFx+a3PcMczr2VcmSR1HMUWBtpMRJwK/IDczcWnpZQ2bOUlAKSUxmzuAUxry3olSVu3a4+u/ObicezdLxcIGhNc8dtnuX2iA5NJEhRfGGj65r9HC8ub2pdvz0Yj4mTg18BC4JiU0is7Vp4kqaPpv0sXfn3x4YwYkBuHICX4zO2TufXJ2RlXJknZK7YwMD0/bemegGH5aUv3FLxFRHwQuA1YAIxPKU3fykskSUWmX201t148jn133ThS8ed//zw/f8jvfiSVtmILAw/kpydExJtqj4ha4AhgDfD4tmwsIs4CbgXmkQsCL27lJZKkItW7popfXTSWA3bbeHL5G3dN5b/vmUZKKcPKJCk7RRUGUkovA/cCQ3jroGBfBWqAm1NKq5saI2JkRLylZ5+IOAe4CZgNHO2lQZLU+fXsVsUtF43lsCG9C20/fuBlvvTHF2hsNBBIKj0VWRewAy4DHgV+GBHHA1OBseTGIJgBfGGT9afmp9HUEBHHkustqIzc2YbzImKTl7E8pfSDVq9ekpSpXbpU8svzD+Pjv5rE/fnRiSc8Pps31tbzP2ccRGV5UX1PJkk7pejCQErp5Yg4BPgauW5A3wO8DlwDfDWltGwbNjOYjWdFzm9hnVnkeheSJHUyXavK+enZY7jqtsn88dnc2AN3Tp7HynUbuO6sMXStKs+4QklqH0X59UdKaU5K6byU0q4ppaqU0uCU0qc2FwRSSpFSik3abmxq38JjSLv9QJKkdldZXsb3z3gbZ48bXGh7YPoiPnrDE6xYs029S0tS0SvKMCBJUmsoKwu+9oH9+MRx+xTanpq5jNOuf5S5y9ZkWJkktQ/DgCSppEUEV54wgi++d1Sh7aWFqzj1ukeZMq+lAe8lqXMwDEiSBFx41FB+eObBVOVvIF64cj1nXP8YD81YlHFlktR2DAOSJOW9/6BB3HTBYezSJde/xuq6Bs6/8Slunzg348okqW0YBiRJambc0D7c/rG3M6hHFwDqGxNX3TaZH973ooOTSep0DAOSJG1i+IBa/vDxIxg5sLbQ9r2/zeDK305mfX1DhpVJUusyDEiStBkDdunCbZcezpH79C20/f6Z1/jwz59g8ar1GVYmSa3HMCBJUgtqu1Ryw7mH8qFD9yi0TZy1jA/86BGmvv5GhpVJUuswDEiStAVVFWV889QD+NL79qUsP4Tla8vXcvpPHuXv/1qQbXGStJMMA5IkbUVEcMGRe/GLcw6le/XGnoYuuvlpfvqPl72xWFLRMgxIkrSNjh3Zn99f9nb26N0VgJTgm3+dxqd+8yxr6uozrk6Stp9hQJKk7TB8QC13XHYEhw7pVWj747PzOPW6R5m1ZHWGlUnS9jMMSJK0nfp0r2bChWM587A9C23T5q/kpGv/yQPTFmZYmSRtH8OAJEk7oLqinG+eegDfPu0Aqspzf07fWFfP+b98ih/e9yKNjd5HIKnjMwxIkrQT/u3QPbnt0sPZNT9icUq5AcouvvlpVqzZkHF1krRlhgFJknbSQXv05E+fOJLDh/YptP196kLee+3DPDN7WYaVSdKWGQYkSWoFfbtXc/MFh3Hx0UMLbXOXreWD1z/Gzx96xcuGJHVIhgFJklpJRXkZ//meUVz/kdHUdsmNR1DfmPjGXVO58KanWba6LuMKJenNDAOSJLWyE/fflbsuP4qD9uhZaLt/2kLe88OHeWrm0gwrk6Q3MwxIktQG9ujdjdsuOZyLjtqr0Pb6inV86GeP8/2/zaC+oTHD6iQpxzAgSVIbqaoo4wvv3ZdfnHMIPbtVAtDQmLjmvhc57frHeHWxg5RJypZhQJKkNnb8qAHcdflRHDakd6Ft8pzlvOeah7nliVmk5M3FkrJhGJAkqR0M6tmVWy8ex3+cOJLK8gBg7YYGvvCHF7jgl0+zcOW6jCuUVIoMA5IktZPysuBjx+zNHy47gmH9uxfa75+2kBN/8DB3Pf96htVJKkWGAUmS2tn+u/XgT584kvOP2Hhz8dLVdVx2yyQuvXmiZwkktRvDgCRJGehSWc6XT9qXCReMZeAuXQrtd0+Zzzu/9xC/mzjXewkktTnDgCRJGTpyWF/uueJoPnToHoW2FWs3cOVtkznvxqeYt3xthtVJ6uwMA5IkZaxH10q+ddqBTLhgLLv36lpof3D6Ik74/kP88tGZNDR6lkBS6zMMSJLUQRw5rC/3fOpozn37ECLX4RCr1tfzlTuncPKPH2HynOXZFiip0zEMSJLUgdRUV3D1+/fjtksOZ2i/mkL786+t4OTrHuGLdzzPijUbMqxQUmdiGJAkqQM6ZEhv/vrJo7jyncOprsj9uU4JJjw+m+P+50FvMJbUKgwDkiR1UNUV5Xzi+GH87YrxHDuiX6F9yeo6rrxtMh+8/jGem+ulQ5J2nGFAkqQObs8+3bjh3EO5/iNjGNRjYzekT89axvt/9Aif/u2zzF/h2ASStp9hQJKkIhARnLj/QP726fFcMn4oleVRWPb7Sa9x7Hcf5Ad/n8HauoYMq5RUbAwDkiQVkZrqCj7/7lH87YrxnLDvgEL72g0N/ODvL3Lsdx/k9olz7YpU0jYxDEiSVISG9K3hZx89hF9dNJZRu+5SaJ//xjquum0y777mIe6ZMt+bjCVtkWFAkqQi9va9+/LnTxzJt049gL7dqwrtMxas4pKbJ3LKdY/y6MuLM6xQUkdmGJAkqciVlwUfOmxPHrjqGC4/fhg1VeWFZc/OWc6Hf/4EZ//iCQctk/QWhgFJkjqJ2i6VfPqdw3nos8dy/hF7UVW+8c/8wy8u5gM/foRzbniSibOWZlilpI7EMCBJUifTp3s1Xz5pXx74zDGcccjulG3seIh/zFjEaT95jLP+93Eef2VJdkVK6hAMA5IkdVK79ezKd04/iHuvGM9JBw0imoWCR15awod+9jhnXP8YD81Y5I3GUokyDEiS1Mnt07871555MH//9HhOHb0b5c1OFTw5cykfveFJ3n3Nw/xu4lzq6hszrFRSezMMSJJUIvbu153vnfE27r9yPB86dA8qmoWCafNXcuVtkznqO/fzkwdfZsXaDRlWKqm9GAYkSSoxg/vU8K3TDuQfnz2Wc98+hK6VG3sfWvDGer599zTe/s37uPrOKbyyaFWGlUpqa4YBSZJK1G49u3L1+/fjsc8fx2feNYJ+tdWFZavrGrjx0Zkc9z//4OxfPME9U+ZT3+AlRFJnU5F1AZIkKVs9u1Xx8WP34cKj9uKPz87jfx9+hRkLNp4RePjFxTz84mIG9ejCh8fuyb8duuebgoOk4hX2HtA2ImLi6NGjR0+cODHrUiRJ2i4pJR5+cTE3PTaL+6ctoHGTjwoVZcHxo/pzxiF7MH54PyrKvdBAytKYMWOYNGnSpJTSmO19rWcGJEnSm0QERw/vx9HD+zF32Rp+9cRsfvPUHJasrgOgvjFxz5QF3DNlAf1qqzlt9O588JDd2btf94wrl7S9PDPQRjwzIEnqTNbXN/DX5+dz8+OzmDhr2WbXGTO4FycfvBvv2X8gfbp7GZHUXjwzIEmS2lR1RTknH7wbJx+8Gy8tXMVtE+fwu4mvsXjV+sI6E2ctY+KsZVx95xSOGtaXD7xtEO/cdyDdq/24IXVUnhloI54ZkCR1dhsaGvnH9EXcNnEO901dSP2mNxcAXSrLOH7UAN6z/64cM6IfNQYDqdV5ZkCSJLW7yvIy3rHvAN6x7wAWr1rPXc+/zp3PzuPpZpcRrdvQyF+ee52/PPc6VRVlHD2sL+/abyDvGDWAXjVVGVYvCQwDkiSpFfTtXs1HDx/CRw8fwpyla/jTc/O489l5TJu/srBOXX0jf5+6kL9PXUh5WTB2r94cN7I/x47sz9C+NUTEFt5BUlvwMqE24mVCkiTB9Pkr+esLr3P3C/PfFAw2tWfvbhwzoh/HjOjH4UP70rWqvMV1Jb2ZlwlJkqQOacTAWkYMrOVT7xjOzMWruWfKfO6ZMp9Js5e/ab3ZS9dw02OzuOmxWVRVlDFuaB+OHdGPI/fpyz79u3vWQGojhgFJktQuhvSt4ZLxe3PJ+L2Zv2IdD0xfyAPTFvLIS4tZXddQWK+uvpGHZizioRmLAOjbvYqxQ/swbmgfDh/ah737eUmR1FoMA5Ikqd0N7NGFMw/bkzMP25O6+kaenrmUB2cs4sHpC5mxYNWb1l28qq5wEzJAv9pqxg3tw7ihvTl0SG/26dedsjLDgbQjvGegjXjPgCRJO+a15Wt5cPpCHp6xmMdfXcLyNRu2uH5tdQVv27MnB+/Zi4P37MnBe/SkZzd7KlLp8J4BSZLUaezWsytnjR3MWWMH09iYmL5gJY+/soTHXl7CE68uZcXaN4eDlevrefjFxTz84uJC29B+NRy8Ry8O2qMH+w3ahVG77kK3Kj/2SJvyqJAkSR1WWVkwatfch/nzjtiLxsbE1Plv8PgrS3nilSVMmr38TaMgN3ll0WpeWbSa302aC0AE7NW3hv0G5cJB7tGD3o51oBJnGJAkSUWjrCzyH+h7cMGRe5FSYu6ytUyavYxnZi/nmdnLmDLvjbeMhpzSxoDwp8nzCu0Ddqlm+IBahvWvZdiA7gzr351hA2rp0bWyvX80KROGAUmSVLQigj16d2OP3t34wNt2A2DdhgamzFvBM7OX88JrK5gy7w1eXrSKxs3cJrngjfUseGP9my4xAuhfmwsJe/erYUjfGob0qWFwn27s3qsbVRVl7fGjSe3CMCBJkjqVLpXljBncmzGDexfa1tY1MG3+G0yZl3v8a94Kps5fSV1942a3sXDlehauXM8/X3pzSCgL2K1XVwb3zoWDppAwuE8Ng3p2obaLZxRUXAwDkiSp0+taVZ7vbahXoa2+oZFZS9fw4oLcKY02AAAQ90lEQVRVvLRwJTMWrOLFhat4edGqFkNCY4I5S9cyZ+la/vnSW5fXVlcwqGdXdu3ZhUE9uzKoR266a4+u7NazKwN6VFNd4ejK6jiKMgxExO7A14ATgT7A68AdwFdTSsu2Yzu9gS8DJwO7AkuAu4Evp5TmtnbdkiSp46goL2Pvft3Zu193YGChvb6hkTnL1jJjwUpmLl7NzCVrmLVkNbOWrGHeirVsqVf2levrmb5gJdMXrGxxnV7dKulXW517dK/e+Ly2mn7duxSe9+xa6fgJanNFFwYiYm/gUaA/8EdgGnAY8EngxIg4IqW0ZBu20ye/neHA/cCvgZHAecB7I+LwlNIrbfNTSJKkjqqivIy9+tawV9+atyxbt6GBucvWMHPxGmbmA8LMJauZs3QN81asa/GMQnPL1mxg2ZoNbxlcbVMR0KNrJb27VdGzWyW9ulXRs1sVvbpV0qtmY1uvblX0qqlkly6V1HapoKaqwhChbVZ0YQC4jlwQuDyldG1TY0R8D7gC+AZw6TZs5/+RCwLfSyld2Ww7lwPX5N/nxFasW5IkFbkuleXs07+WffrXvmVZSomlq+uYt3wd81asZd7ytby+Yh2vLV/L68vXMm/5OhauXLfZG5k3JyVYvmbDVgdd21QEdK+qoLZLBbVdKuneZePz2i4V1Fbn5muqK+hWVU7Xqgq6VZbTtSr36FZVTrfKio3zleWGi06sqEYgzp8VeAmYCeydUmpstqyW3OVCAfRPKa3ewna6AwuBRmDXlNLKZsvKgFeAwfn32KGzA45ALEmSNlXf0MjSNXUsWrl+42PV+s3Or1xXn3W5BdUVZbmQUFVBl8oyqivKqaooo6qijOr8I/e8nKryMqory6gqb9bWbN3mr6koK6O8PKgsK6O8LKgsj/w0N19RFlSUl+WnkW8ro6I8v6wst6zUw0opjUB8bH56b/MgAJBSWhkRjwAnAOOA+7awnXFA1/x23nRRX0qpMSLuAS7Ov5+XCkmSpFZRUV5G/9ou9K/tstV1NzQ05s8M1OUvLap78/PVTW256RvrNrByXT1r6hpave719Y2sr29k2XaepWgvZUEuWDQLDeURRARlAWVN07LY+DwiP5973rRuedlmXhf515VtXLd8k9flnufOzPz36QdRU10cH7OLo8qNRuSnM1pY/iK5MDCcLYeBbdkO+e1sUUS09NX/yK29VpIkqSWV5WWFm4m3R31DI6vXNxTCwar19azMP1/Z7Pnq9fWsrWtgzYaG3LQuP59/rNuQm67d0PrhorU1JqhraIQGoAPklW+eemDWJWyzYgsDPfLTFS0sb2rv2U7bkSRJ6lAqysvo0a2MHt1aZ8yDxsbEuvp8MMiHg7r8mYL19bnnTfMbpw3UNTSyfkMjdQ2NzdZvep57XX1jyj0acs8bmj2vb0jUNzbS0JjY0JBf1rj5ZR1NFNFVS8UWBjqclq7Nyp8xGN3O5UiSJLWqsrKgW1UF3ao65sfGlBKNKXdZVUM+XDQ0JhpT7pEShfmUyLfn2ppe27RuY2Oz5ym37dxrN75PQ2G7b14/t21IJLpWFs9YEh1zr7as6Rv7Hi0sb2pf3k7bkSRJUoaart8vLyueD+AdSVnWBWyn6flpS9fyD8tPW7oXoLW3I0mSJBWtYgsDD+SnJ+S7AC3Idy16BLAGeHwr23kcWAsckX9d8+2UkbsJufn7SZIkSZ1OUYWBlNLLwL3AEODjmyz+KlAD3Nx8jIGIGBkRb+rZJ6W0Crg5v/7Vm2zn3/Pbv8cRiCVJktSZFds9AwCXAY8CP4yI44GpwFhyYwLMAL6wyfpT89NN7+v+T+AY4NMR8TbgSWAU8AFyA5JtGjYkSZKkTqWozgxA4ezAIcCN5ELAlcDewDXAuJTSkm3czhLgcOCHwD757YwF/g8Yk38fSZIkqdMqxjMDpJTmAOdt47ot9vSaUloKfDL/kCRJkkpK0Z0ZkCRJktQ6DAOSJElSiTIMSJIkSSXKMCBJkiSVKMOAJEmSVKIMA5IkSVKJMgxIkiRJJcowIEmSJJUow4AkSZJUogwDkiRJUomKlFLWNXRKEbGka9euvUeNGpV1KZIkSerEpk6dytq1a5emlPps72sNA20kIl4FdgFmZvD2I/PTaRm8tzbPfdIxuV86HvdJx+R+6XjcJx1TVvtlCPBGSmmv7X2hYaATioiJACmlMVnXohz3Scfkful43Ccdk/ul43GfdEzFuF+8Z0CSJEkqUYYBSZIkqUQZBiRJkqQSZRiQJEmSSpRhQJIkSSpR9iYkSZIklSjPDEiSJEklyjAgSZIklSjDgCRJklSiDAOSJElSiTIMSJIkSSXKMCBJkiSVKMOAJEmSVKIMA51IROweETdExLyIWB8RMyPiBxHRK+vaSlH+959aeMzPur7OLCJOj4hrI+LhiHgj/zufsJXXvD0i7oqIpRGxNiKei4hPRUR5e9Xd2W3PfomIIVs4flJE/Lq96+9sIqJPRFwYEX+IiJfy/+5XRMQ/I+KCiNjsZwSPlba1vfvFY6V9RMS3I+K+iJiT3ydLI+KZiPhKRPRp4TVFcaxUZF2AWkdE7A08CvQH/ghMAw4DPgmcGBFHpJSWZFhiqVoB/GAz7avau5AS80XgIHK/57nAyC2tHBEfAH4HrAN+AywFTgK+DxwBfLAtiy0h27Vf8iYDd2ym/YVWrKtUfRD4CfA68AAwGxgAnAr8L/DuiPhgajY6qcdKu9ju/ZLnsdK2rgAmAX8DFgI1wDjgauDiiBiXUprTtHJRHSspJR+d4AHcAyTgE5u0fy/ffn3WNZbaA5gJzMy6jlJ8AMcCw4AAjskfAxNaWHcXcv+xrwcOadbehVzATsCHsv6ZOsNjO/fLkPzyG7Ouu7M+gOPIfTgp26R9ILkPoAk4rVm7x0rH3C8eK+2zX7q00P6N/O//umZtRXWseJlQJ5A/K3ACuQ+fP95k8VeA1cDZEVHTzqVJmUgpPZBSejHl//fditOBfsCvU0pPN9vGOnLfZAN8rA3KLDnbuV/UxlJK96eU/pRSatykfT5wfX72mGaLPFbawQ7sF7WD/L/zzfltfjqsWVtRHSteJtQ5HJuf3ruZ/zxWRsQj5MLCOOC+9i6uxFVHxEeAPcmFsueAh1JKDdmWpWaOy0/v3syyh4A1wNsjojqltL79ylLeoIi4BOgDLAEeSyk9l3FNpWBDflrfrM1jJXub2y9NPFaycVJ+2vx3XVTHimGgcxiRn85oYfmL5MLAcAwD7W0gcPMmba9GxHkppX9kUZDeosXjJ6VUHxGvAvsBQ4Gp7VmYAHhn/lEQEQ8C56SUZmdSUScXERXAR/OzzT/MeKxkaAv7pYnHSjuIiKuA7kAP4BDgSHJB4FvNViuqY8XLhDqHHvnpihaWN7X3bIdatNH/AceTCwQ1wAHAT8ld3/nXiDgou9LUjMdPx7QG+C9gDNAr/xhP7obKY4D7vPSxzXwL2B+4K6V0T7N2j5VstbRfPFba11XkLsH+FLkgcDdwQkppUbN1iupYMQxIbSSl9NX8tZ8LUkprUkovpJQuJXdTd1dyPRBI2oyU0sKU0pdTSpNSSsvzj4fIneV8AtgHuDDbKjufiLgcuJJcj3RnZ1yO8ra0XzxW2ldKaWBKKch90XcquW/3n4mI0dlWtuMMA51DU8Ls0cLypvbl7VCLtq7pBrCjM61CTTx+ikhKqZ5c94rgMdSqIuLfgWuAfwHHppSWbrKKx0oGtmG/bJbHStvKf9H3B3Khqw9wU7PFRXWsGAY6h+n56fAWljfd4d7SPQVqX02nEj1t2zG0ePzkr9Hdi9zNeq+0Z1HaIo+hVhYRnwKuJdcn/bH5nms25bHSzrZxv2yJx0obSynNIhfU9ouIvvnmojpWDAOdwwP56QmbGZmwltzgFmuAx9u7MG3WuPy0Q/wnIO7PT0/czLKjgW7Aox2hxwcVeAy1ooj4D3IDIT1L7gPnwhZW9VhpR9uxX7bEY6V9DMpPm3oKLKpjxTDQCaSUXgbuJXdj6sc3WfxVct8I3JxSWt3OpZWsiBi1uRu2ImII8KP87IT2rEktuh1YDHwoIg5paoyILsDX87M/yaKwUhYRozf9ciPffjy5kUDBY2inRcSXyN2YOhE4PqW0eAure6y0k+3ZLx4rbS8ihkfEWy75iYiyiPgG0J/ch/tl+UVFdayEY790DvmBxx4l9w/yj+S6qhpLbgyCGcDbU0pLsquwtETE1eRu9noImAWsBPYG3ktuBMK7gFNSSnVZ1diZRcTJwMn52YHAu8h9M/Zwvm1xSumqTda/ndyw8b8mN2z8+8l1D3c7cIYDZe287dkv+S4Rh5H7f21ufvmBbOy/+0sppaY/qtoBEXEOcCO5bzOvZfM9n8xMKd3Y7DUeK21se/eLx0rby1+u9U3gn8Cr5MZxGECu16ahwHxyoe1fzV5TNMeKYaATiYg9gK+ROy3VB3gd+APw1WZpVe0gIsYDlwIHs7Fr0eXkTvfeTO5MjQdfG8mHsa9sYZVZKaUhm7zmCOALwOHkAttLwA3ADx0krnVsz36JiAuAU8h1pdgXqAQWAI8BP0opPdzSRrRttmF/APwjpXTMJq/zWGlD27tfPFbaXkTsT+5v+pHA7uS6BF1N7svWv5D7t/+WG7uL5VgxDEiSJEklynsGJEmSpBJlGJAkSZJKlGFAkiRJKlGGAUmSJKlEGQYkSZKkEmUYkCRJkkqUYUCSJEkqUYYBSZIkqUQZBiRJkqQSZRiQJEmSSpRhQJIkSSpRhgFJUpuIiGMiIkXE1VnXIknaPMOAJGmHRcSQ/Af+G7OuRZK0/SqyLkCS1Gk9CYwCFmddiCRp8wwDkqQ2kVJaA0zLug5JUsu8TEiStEPy9wK8mp89J3+5UNPj3JbuGYiIB/PtlRHx5Yh4OSLWRcT0iLio2XqXRsTzEbE2IuZGxFcjYrN/tyJibETcHhHzI6IuIuZExE8jYlBb/fyS1Bl4ZkCStKMeBHoCnwQmA3c0W/ZsftmW/BoYC9wFbABOB34WERuAA4FzgD8D9wHvB74MrAG+3XwjEXE+8DNgPXAnMAcYBlwInBQR41JKs3f0h5SkzixSSlnXIEkqUhExhNzZgV+mlM7dZNkxwAPAV1NKVzdrfxAYDzwNvDOltDzfPpTcZUWrgeXAkSml1/LLegIvAQnYNaVUn28fDrwAzAbGN62fX3Y8cC9wZ0rplFb9wSWpk/AyIUlSVj7XFAQAUkqvAP8kd0bhv5p/sM+v9yegL7Bbs218DKgEPtl8/fxr7iN3puCkiKhts59CkoqYlwlJkrLy9Gba5uWnEzezrOnD/u7ArPzzw/PT8RFx6GZe0x8oB4a3sE1JKmmGAUlSJlJKKzbTXJ+fbmlZZbO2PvnpZ7bydt23ozRJKhmGAUlSMWsKDT1SSm9kWokkFSHvGZAk7YyG/LQ8o/d/PD89KqP3l6SiZhiQJO2MZeR6+Nkzo/f/EbluSb+f71noTSKiKiIMCpLUAi8TkiTtsJTSqoh4AjgqIm4BZpA7W3BnO73/tPw4AzcAUyLi7nwNleQCylHAImBke9QjScXGMCBJ2llnA98HTgTOBAKYC8xsjzdPKU2IiMnAlcCxwAnkxiqYB9wO/KY96pCkYuSgY5IkSVKJ8p4BSZIkqUQZBiRJkqQSZRiQJEmSSpRhQJIkSSpRhgFJkiSpRBkGJEmSpBJlGJAkSZJKlGFAkiRJKlGGAUmSJKlEGQYkSZKkEmUYkCRJkkqUYUCSJEkqUYYBSZIkqUQZBiRJkqQSZRiQJEmSSpRhQJIkSSpRhgFJkiSpRP1/t9J9EX50t2IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 277,
       "width": 385
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "time = 5.0\n",
    "x = np.linspace(0, 30, 300)\n",
    "y = [np.exp(-H2(results.x[1:], _)) for _ in x]\n",
    "plt.plot(x, y)\n",
    "plt.title(\"Estimated secondary shelf life survival function\" );\n",
    "plt.xlabel(\"time\")\n",
    "plt.ylabel(\"survival\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lifelines import WeibullFitter, ExponentialFitter\n",
    "# only primary shelf life dataset - True iif E==true and obs_tau==False\n",
    "\n",
    "ef = ExponentialFitter()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.tail(25)\n",
    "\n",
    "df_primary = df.copy()\n",
    "df_primary['E'] = (df_primary['E'] & ~df['obs_tau'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>model</th>\n",
       "      <td>lifelines.ExponentialFitter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of observations</th>\n",
       "      <td>1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of events observed</th>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log-likelihood</th>\n",
       "      <td>-170.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hypothesis</th>\n",
       "      <td>lambda_ != 1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coef</th>\n",
       "      <th>se(coef)</th>\n",
       "      <th>coef lower 95%</th>\n",
       "      <th>coef upper 95%</th>\n",
       "      <th>z</th>\n",
       "      <th>p</th>\n",
       "      <th>-log2(p)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lambda_</th>\n",
       "      <td>421.49</td>\n",
       "      <td>81.06</td>\n",
       "      <td>262.61</td>\n",
       "      <td>580.36</td>\n",
       "      <td>5.19</td>\n",
       "      <td>&lt;0.005</td>\n",
       "      <td>22.16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
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       "<IPython.core.display.HTML object>"
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   ],
   "source": [
    "ef.fit(df_primary['T_obs'], df_primary['E']).print_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <tbody>\n",
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       "      <th>model</th>\n",
       "      <td>lifelines.WeibullFitter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of observations</th>\n",
       "      <td>749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of events observed</th>\n",
       "      <td>443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log-likelihood</th>\n",
       "      <td>-1422.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hypothesis</th>\n",
       "      <td>lambda_ != 1, rho_ != 1</td>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coef</th>\n",
       "      <th>se(coef)</th>\n",
       "      <th>coef lower 95%</th>\n",
       "      <th>coef upper 95%</th>\n",
       "      <th>z</th>\n",
       "      <th>p</th>\n",
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       "      <th>lambda_</th>\n",
       "      <td>12.70</td>\n",
       "      <td>0.26</td>\n",
       "      <td>12.18</td>\n",
       "      <td>13.21</td>\n",
       "      <td>44.55</td>\n",
       "      <td>&lt;0.005</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rho_</th>\n",
       "      <td>2.31</td>\n",
       "      <td>0.08</td>\n",
       "      <td>2.14</td>\n",
       "      <td>2.47</td>\n",
       "      <td>15.87</td>\n",
       "      <td>&lt;0.005</td>\n",
       "      <td>186.10</td>\n",
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   "source": [
    "\n",
    "df_secondary = df.copy()\n",
    "df_secondary = df_secondary[df_secondary['obs_tau']]\n",
    "df_secondary['T'] = df_secondary['T_obs'] - df_secondary['tau']\n",
    "\n",
    "wf = WeibullFitter()\n",
    "wf.fit(df_secondary['T'], df_secondary['E']).print_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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